Optical fiber transmissions employing coherent detection make it possible to achieve very high data rates over long distances, e.g. typically 100 Gb/s per wavelength channel. However coherent detection solutions may be too expensive for some applications, e.g. short reach transmissions. Therefore a need exists for optical transmission techniques that achieve a high data rate and remain compatible with direct detection of the signal intensity, i.e. quadratic detection, at the destination node.